ABSTRACT Context. A mid-infrared nulling-space interferometer offers a promising way to characterize thermal light from habitable planet candi- dates around Su

ABSTRACT Context. A mid-infrared nulling-space interferometer offers a promising way to characterize thermal light from habitable planet candi- dates around Sun-like stars. However, one of the main challenges inherent in achieving this ambitious goal is the high-precision stability of the optical path difference and amplitude over a few days for planet detections and all the way up to a few weeks for in-depth char- acterization. This is related to mission parameters such as aperture size, number of apertures, and total instrument throughput. Aims. Here, we propose a new method called phase-space synthesis decomposition (PSSD) to shorten the stability requirement to a scale of minutes, significantly relaxing the technological challenges of the mission. Methods. By focusing on the consideration of what exactly modulates the planetary signal in the presence of the stellar leak and sys- tematic error, PSSD prioritizes the modulation of the signals along the wavelength domain rather than baseline rotation. Modulation along the wavelength domain allows us to extract source positions in parallel to the baseline vector for each exposure. The sum of the one-dimensional data is converted into two-dimensional information. Based on the reconstructed image, we constructed a continuous equation and extract the spectra through the singular value decomposition, while efficiently separating them from a long-term system- atic stellar leak. Results. We performed numerical simulations to investigate the feasibility of PSSD for the Large Interferometer For Exoplanets (LIFE) mission concept. We confirm that multiple terrestrial planets in the habitable zone around a Sun-like star at 10 pc can be detected and characterized despite high levels and long durations of systematic noise. We also find that PSSD is more robust against a sparse sampling of the array rotation compared to purely rotation-based signal extraction. Using PSSD as signal extrac- tion method significantly relaxes the technical requirements on the signal stability and further increases the feasibility of the LIFE mission.